- olympiad@cscacademy.org

- 1. This is Model Question Paper.
- 2. This is an Online Worksheet.
- 3. Total Questions-50.
- 4. Total Time-60 minutes.

**Section-1-Mathematical Thinking:**

**Q.1**- **The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is:**

(a) 30

(b) 33

(c) 36

(d) 45

**Q.2**- **Which of the following numbers should be added to 11158 to make it exactly divisible by 77?**

(a) 9

(b) 8

(c) 6

(d) 7

**Q.3- ****If 45% of a number is added to the another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers?**

(a) 8:7

(b) 3:2

(c) 7:8

(d) None of these

**Q.4- ****The sum of all prime numbers between 30 and 42 is:**

(a) 103

(b) 109

(c) 105

(d) 104

**Q.5- ****If the number formed by the last two digits of a three digit integer is an integral multiple of 6% the original integer itself will always be divisible by**:

(a) 6

(b) 3

(c) 2

(d) 12

** **

**Section-****2****-** **Application Mathematics:**

**Q.6- ****The sum of two numbers is 2490 and if 6.5% of one number is equal to 8.5% of the other, then numbers are-**

(a)1414, 1076

(b)1411, 1079

(c)1412, 1078

(d)None of these

**Q.7- ****If OA and OB are opposite rays; a ray OC inclined. If one of the angle is 75°, then the measurement of the second angle is:**

(a) 105°

(b) 70°

(c) 15°

(d) None of the above

**Q.8**- **Two parallel lines are cut by a transversal, then which of the following are true?**

- Pair of alternate interior angles are congruent.
- Pair Of corresponding angles are congruent.
- Pair of interior angles on the same side of the transversal are supplementary.

(a) 1, 2, 3 are true

(b) 1 and 3 are true

(c) 1 and 2 are true

(d) 2 and 3 are true

**Q.9- ****The radius of the incircle of a triangle whose sides are 9 cm, 12 cm and 15 cm is___**

(a) 9 cm

(b) 13 cm

(c) 3 cm

(d) 6 cm

**Q.10- ****Find measure of central angle of the sector whose perimeter is 25 cm and radius of the circle is 7 cm?**

(a) 45°

(b) 22.5°

(c) 135°

(d) 90°

**Section-****3****- Logical Thinking: **

**Q.11**- **Rajan started from his house and went 2 km East, then he turned right and went 3 km, again turned right and went 3 km, again he turned right and covered 1 km and finally after turning right and going 1 km he reached point K. In which direction was Rajan walking when he reached K?**

(a) East

(b) South

(c) West

(d) North

**Q.12- ****In the following question, number of letters skipped in between adjacent letters of the series starting from behind increased by one. Which of the following observes the rule?**

(a) OLGDC

(b) ONLKJ

(c) OMKIG

(d) OMJFA

**Q.13- ****A’s mother is sister of B and has a daughter C. How can A be related to B from among the following?**

(a) Uncle

(b) Niece

(c) Daughter

(d) Father

**Section-****4****- High Order Thinking (HOT)**

**Q.14- ****Mohan gets 3 marks for each correct sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums solved correctly is-**

(a) 25

(b) 10

(c) 15

(d) 20

**Q.15- ****If x/y = 4/9, then what is the value of (7x ^{2}-19xy+11y^{2})/y^{2}?**

(a) 59/81

(b) 100/27

(c) 319/81

(d) 913/81